Numerical Integration

Trapezoidal Approximation

Trapezoidal Method

Used to estimate area under a curve

divide a region under a curve into trapezoids

x0, x1, x2,… represent the beginning of each sub-interval

Trapezoidal Rule

Where n is the number of sub-intervals between a and b

Parts:

n

b

a

xfxfxfxfn

abdxxf

210 222

n

ab

2

→ calculate from given intervals

nxxx ,,, 10 → the starting x-value of each sub-interval

1, 2, 2, 2,…, 1 → coefficients in trapezoidal rule

Example: Approximate area under y = 1 + x3 using n = 4

1

0

31 dxx

0 ¼ ½ ¾ 1

Estimate the area using n = 8

Let’s Practice